In this paper, all graphs considered are finite and simple. For a
real number \(x\) , \(\lceil x\rceil \)  is the least integer not less than
\(x\)  and \(\lfloor x \rfloor \)  is the largest integer not larger than
\(x\) . We use \(V(G)\) , \(E(G)\) , \(\delta (G)\)  and \(\Delta (G)\)  to denote
the vertex set, edge set, minimum degree and maximum degree of \(G\) ,
respectively. For a vertex \(v \in V(G)\) , let \( N_G(v)\)  denote the
set of neighbors of \(v\)  in \(G\)  and \(d_G(v)=|N_G(v)|\)  denote the
degree of \(v\) . We use \(d(v)\)  instead of \(d_G(v)\)  for brevity. For
other undefined concepts, we refer the reader to [1]}.
